# Inference under Covariate-Adaptive Randomization with Multiple Treatments

arXiv: https://arxiv.org/abs/1806.04206 · HTML: https://mlsanity.com/paper/1806.04206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2018.

## Built on by (most cited first, 2 of 2)

- [On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization](https://mlsanity.com/paper/2506.05945/) (2025)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)

## Abstract (arXiv)

This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specifically, we study inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni et al. (2018), covariate-adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve balance within each stratum. In contrast to Bugni et al. (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a fully saturated linear regression, i.e., a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are invalid; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with strata fixed effects, i.e., a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity-consistent estimator of the asymptotic variance are conservative, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact. A simulation study illustrates the practical relevance of our theoretical results.